Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $\mathrm{Ek}<{10}^{-6}$. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($\mathrm{Ra}=0.7{\mathrm{Ra}}_{\mathrm{crit}}$ in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Péclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.

• Received 17 January 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.094501